CROSSTALK IN COAXIAL CABLES 349 



From equations (20) and (21) above, we have 



Pi = 



Qi = 

 P2 = 



<22 = 



2X1(1 — 771172) (ti — t) 



— -^13 



2Ki(l — 171772) (71 + 7) 



Z\z,-q2 



2X2(1 — 771772) (72 — 7) 



2X2(1 — 771772) (72 + 7) 

 If we designate 



by \l/i 



Ki{l — 771772) (71^ — 7^) 

 and 



-^13^2 , . 



X2(l -77l772)(72^-7^)^"^" 



we have 



/i = aig-T'^ — iigTi^ + 772a2C~'^2'' 



- 77262^^^^ + ('/'171 + 1^277 272) e-T^ (31) 



I2 = 77iaie-' I'l^ — 77i&ig'>'i=' + aie~'^-^'' 



- biey^' + (i/'i77i7i + i/'272)e-^^ (32) 



Vi = Kiaie-y^"" + Xi^ieTi^ - 771X2^2^-^2* 



- 771X2626^^" + (i/'iXi7 - 1^2X277 17) e-T-, (33) 



V2 = - 772Xiaie-Ti^ — 772Xi&igTi^ + Kiaie--*^" 



+ Kib.e''^'' - (i/'iXi7727 - yp2K2y)e-y\ (34) 



Before proceeding with the appUcation of these results to specific 

 crosstalk problems, we will establish certain relations which, as in the 

 single-tertiary analysis, will be fundamental in relating crosstalk 

 measurements on short lengths of cable to the crosstalk to be expected 

 in a longer length. 



Let us consider the crosstalk as measured on a short length under 



the following two conditions: (1) both tertiaries open and (2) tertiary 



1 short-circuited at each end and tertiary 2 open. We will designate 



the crosstalk under condition (1) by XI and under condition (2) by 



Xl{\ — ^). Under condition (2) the tertiary current (/i) for unit 



Z 

 current in the energized coaxial is given by -^ and the indirect cross- 



talk current in the disturbed coaxial is thus ^^ , so that we have 



